- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2006-07-09 07:28:41+12:00
- Desc:
- committing version01 of dokos_celler_lovell_1996
- Permanent Source URI:
- http://models.cellml.org/workspace/dokos_celler_lovell_1996/rawfile/cf933b2e61b4c222e177d14130b483851451b852/dokos_celler_lovell_1996.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : dokos_model_1996.xml
CREATED : 10th April 2003
LAST MODIFIED : 20th April 2005
AUTHOR : Catherine Lloyd
Department of Engineering Science
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/01/2002 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Dokos et al's 1996 mathematical model of the ion currents underlying sinoatrial node pacemaker activity.
CHANGES:
04/06/2003 - CML - Fixed MathML in a couple of components.
11/08/2003 - CML - Added equations.
20/04/2005 - PJV - Made MathML id's unique
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="dokos_celler_lovell_1996_version01" name="dokos_celler_lovell_1996_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>A Single Cell Mathematical Model of the Ion Currents Underlying Sinoatrial Node Pacemaker Activity</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
Sinoatrial (SA) node cells have an inherent ability to generate a depolarising, unstable resting potential leading to automaticity. The rhythmic, electrical activity of the sinoatrial cells set the rate at which the entire heart beats, hence the sinoatrial node myocytes are referred to as the pacemaker cells. The mechanism underlying this automaticity is a net inward ion flux, which immediately follows the action potential repolarisation phase. The relative contributions of the various ionic currents involved in this net ionic influx are the subject of a study by Socrates Dokos, Branko Celler and Nigel Lovell (1996). Using Hodgkin-Huxley (<ulink url="${HTML_EXMPL_HHSA_INTRO}">The Hodgkin-Huxley Squid Axon Model, 1952</ulink>) type formulations of gated membrane currents, they develop a single cell mathematical model of the ion currents underlying sinoatrial node pacemaker activity (the complete original paper reference is cited below).
</para>
<para>
In their paper they review the existing theories of pacemaker generation. These include:
<itemizedlist>
<listitem>
<para>The idea that pacemaker potential is primarily due to the decline of the outward delayed rectifier current, <emphasis>i<subscript>K</subscript>
</emphasis>, which uncovers a background inward current, leading to membrane depolarisation.</para>
</listitem>
<listitem>
<para>The hypothesis that pacemaker activity arises from a time-dependent inward current, such as the hyperpolarisation-activated current,<emphasis>i<subscript>f</subscript>
</emphasis>.</para>
</listitem>
<listitem>
<para>The idea that the L-type Ca<superscript>2+</superscript> current <emphasis>i<subscript>Ca,L</subscript>
</emphasis>, supplies the inward flux for pacemaker depolarisation.</para>
</listitem>
</itemizedlist>
</para>
<para>
Earlier efforts to simulate the pacemaker activity of the SA node cells include mathematical models developed by <ulink url="${HTML_EXMPL_NN_SAN_MODEL}">Noble and Noble, 1984</ulink>, and <ulink url="${HTML_EXMPL_D_SAN_MODEL}">Demir <emphasis>et al.</emphasis>, 1994 </ulink>. (Since this model was published in 1996, other SA node models have been developed, including: <ulink url="${HTML_EXMPL_D99_SAN_MODEL}">Demir <emphasis>et al.</emphasis>, 1999</ulink>, <ulink url="${HTML_EXMPL_Z_SAN_MODEL}">Zhang <emphasis>et al.</emphasis>, 2000</ulink>, and <ulink url="${HTML_EXMPL_B_SAN_MODEL}">Boyett <emphasis>et al.</emphasis>, 2001</ulink>). However, despite the developments in enzyme isolation techniques which have led to the improved characterisation of SA node currents, the single cell mathematical models which have been developed are significantly different from each other. In addition, despite the relatively large number of models, none specifically focus on the ionic currents underlying the various phases of the mammalian SA node pacemaker action potential.
</para>
<para>
This has become the focus of the Dokos <emphasis>et al.</emphasis> 1996 model, which is based on experimental data recorded in isolated rabbit SA node myocytes, and taken from a number of different published studies. The model is an extension of previously published SA cell models (see above), and the complete cell model (see <xref linkend="fig_cell_diagram"/> below) includes nine membrane currents which interact to generate spontaneous pacemaker activity. The model also includes variations in extracellular and cytosolic ion concentrations, and ion fluxes between the cytosol and the sarcoplasmic reticulum.
</para>
<para>
Model simulations suggest that the main ion current underlying pacemaker activity is the inward background sodium current <emphasis>i<subscript>b,Na</subscript>
</emphasis>. The decay of the delayed rectifying K<superscript>+</superscript> current <emphasis>i<subscript>K</subscript>
</emphasis>, and the presence of the hyperpolarisation-activated current <emphasis>i<subscript>f</subscript>
</emphasis>, were insignificant, and were not essential to pacemaker activity.
</para>
<para>
<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WMD-45MGSGP-2R&_coverDate=08%2F07%2F1996&_alid=85735248&_rdoc=1&_fmt=&_orig=search&_qd=1&_cdi=6932&_sort=d&view=c&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=5a9a780e34062d656a66722a6447ce48">Ion Currents Underlying Sinoatrial Node Pacemaker Activity: A New Single Cell Mathematical Model</ulink>, Socrates Dokos, Branko Celler, and Nigel Lovell, 1996, <ulink url="http://www.sciencedirect.com/science?_ob=JournalURL&_cdi=6932&_auth=y&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=c8e64d20ff203cda2255f4b6b7affe4f">
<emphasis>Theoretical Journal of Biology</emphasis>
</ulink>, 181, 245-272. (A PDF version of the article is available to subscribers of the Theoretical Journal of Biology.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=8869126&dopt=Abstract">PubMed ID: 8869126</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram</title>
</objectinfo>
<imagedata fileref="cell_diagram.gif"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram of the Dokos <emphasis>et al.</emphasis> 1996 mathematical model of the SA node cell. Sodium, calcium and potassium ions are exchanged between the intracellular and extracellular environments through channels, the sodium-potassium pump and the sodium-calcium exchanger. Calcium is transferred between the cytosol and the sarcoplasmic reticulum (SR), and between the local regions of the SR.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!--
Below, are defined some additional units for association with variables and
constants within the model.
-->
<units name="first_order_rate_constant">
<unit units="second" exponent="-1"/>
</units>
<units name="second_order_rate_constant">
<unit units="second" exponent="-1"/>
<unit units="millimolar" exponent="-1"/>
</units>
<units name="millivolt">
<unit units="volt" prefix="milli"/>
</units>
<units name="per_millivolt">
<unit units="volt" prefix="milli" exponent="-1"/>
</units>
<units name="per_millivolt_second">
<unit units="millivolt" exponent="-1"/>
<unit units="second" exponent="-1"/>
</units>
<units name="nanoS">
<unit units="siemens" prefix="nano"/>
</units>
<units name="picoF">
<unit units="farad" prefix="pico"/>
</units>
<units name="picoA_per_millimolar">
<unit units="ampere" prefix="pico"/>
<unit units="millimolar" exponent="-1.59"/>
</units>
<units name="picoA">
<unit units="ampere" prefix="pico"/>
</units>
<units name="millimolar">
<unit units="mole" prefix="milli"/>
<unit units="litre" exponent="-1"/>
</units>
<units name="joule_per_mole_kelvin">
<unit units="joule"/>
<unit units="mole" exponent="-1"/>
<unit units="kelvin" exponent="-1"/>
</units>
<units name="coulomb_per_millimole">
<unit units="coulomb" exponent="-1"/>
<unit units="mole" prefix="milli"/>
</units>
<units name="picolitre">
<unit units="litre" prefix="pico"/>
</units>
<component name="environment">
<variable units="second" public_interface="out" name="time"/>
</component>
<component name="constants">
<variable units="joule_per_mole_kelvin" public_interface="out" name="R" initial_value="8.32"/>
<variable units="kelvin" public_interface="out" name="T" initial_value="310.0"/>
<variable units="coulomb_per_millimole" public_interface="out" name="F" initial_value="96.49"/>
</component>
<component name="membrane">
<variable units="millivolt" public_interface="out" name="E" initial_value="-64.9"/>
<variable units="picoF" name="C" initial_value="32.0"/>
<variable units="picoA" name="i_tot"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="picoA" public_interface="in" name="i_CaL"/>
<variable units="picoA" public_interface="in" name="i_CaT"/>
<variable units="picoA" public_interface="in" name="i_Na"/>
<variable units="picoA" public_interface="in" name="i_K"/>
<variable units="picoA" public_interface="in" name="i_f"/>
<variable units="picoA" public_interface="in" name="i_p"/>
<variable units="picoA" public_interface="in" name="i_NaCa"/>
<variable units="picoA" public_interface="in" name="i_bNa"/>
<variable units="picoA" public_interface="in" name="i_bK"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="membrane_voltage_diff_eq">
<eq/>
<apply>
<diff/>
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<ci> time </ci>
</bvar>
<ci> E </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> i_tot </ci>
</apply>
<ci> C </ci>
</apply>
</apply>
<apply id="i_tot_calculation">
<eq/>
<ci> i_tot </ci>
<apply>
<plus/>
<ci> i_CaL </ci>
<ci> i_CaT </ci>
<ci> i_Na </ci>
<ci> i_K </ci>
<ci> i_f </ci>
<ci> i_p </ci>
<ci> i_NaCa </ci>
<ci> i_bNa </ci>
<ci> i_bK </ci>
</apply>
</apply>
</math>
</component>
<component name="reversal_potentials">
<variable units="millivolt" public_interface="out" name="E_Ca"/>
<variable units="millivolt" public_interface="out" name="E_Na"/>
<variable units="millivolt" public_interface="out" name="E_K"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Cai"/>
<variable units="millimolar" public_interface="in" name="Cao"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="E_Ca_calculation">
<eq/>
<ci> E_Ca </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
</apply>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Cao </ci>
<ci> Cai </ci>
</apply>
</apply>
</apply>
</apply>
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<eq/>
<ci> E_Na </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Nao </ci>
<ci> Nai </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="E_K_calculation">
<eq/>
<ci> E_K </ci>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<ln/>
<apply>
<divide/>
<ci> Ko </ci>
<ci> Ki </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="L_type_calcium_current">
<variable units="picoA" public_interface="out" name="i_CaL"/>
<variable units="nanoS" name="g_CaL" initial_value="400.0"/>
<variable units="millivolt" public_interface="in" name="E_Ca"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="E"/>
<variable units="millimolar" public_interface="in" private_interface="out" name="Cai"/>
<variable units="dimensionless" private_interface="in" name="d"/>
<variable units="dimensionless" private_interface="in" name="f"/>
<variable units="dimensionless" private_interface="in" name="f2"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_CaL_calculation">
<eq/>
<ci> i_CaL </ci>
<apply>
<times/>
<ci> g_CaL </ci>
<ci> d </ci>
<ci> f </ci>
<ci> f2 </ci>
<apply>
<plus/>
<ci> E </ci>
<apply>
<minus/>
<ci> E_Ca </ci>
</apply>
<cn cellml:units="millivolt"> 75.0 </cn>
</apply>
</apply>
</apply>
</math>
</component>
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<variable units="second" name="tau_d" initial_value="0.002"/>
<variable units="millivolt" public_interface="in" name="E"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="L_type_calcium_current_d_gate_d_infinity_calculation">
<eq/>
<ci> d_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> E </ci>
<cn cellml:units="millivolt"> 6.6 </cn>
</apply>
<cn cellml:units="millivolt"> -6.6 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="L_type_calcium_current_d_gate_dd_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> d </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> d_infinity </ci>
<ci> d </ci>
</apply>
<ci> tau_d </ci>
</apply>
</apply>
</math>
</component>
<component name="L_type_calcium_current_f_gate">
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<variable units="second" name="tau_f"/>
<variable units="millivolt" public_interface="in" name="E"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<apply>
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<divide/>
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<cn cellml:units="millivolt"> 6.0 </cn>
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<cn cellml:units="dimensionless"> 1.0 </cn>
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<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> E </ci>
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<cn cellml:units="millivolt"> 8.1 </cn>
</apply>
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<divide/>
<apply>
<minus/>
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<ci> f </ci>
</apply>
<ci> tau_f </ci>
</apply>
</apply>
</math>
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<variable units="millivolt" public_interface="in" name="E"/>
<variable units="millimolar" public_interface="in" name="Cai"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<apply>
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<ci> f2 </ci>
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<apply>
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<ci> Cai </ci>
<ci> f2 </ci>
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</apply>
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<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="E"/>
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<variable units="dimensionless" private_interface="in" name="f"/>
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<ci> g_CaT </ci>
<ci> d </ci>
<ci> f </ci>
<apply>
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<apply>
<minus/>
<ci> E_Ca </ci>
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<cn cellml:units="millivolt"> 75.0 </cn>
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<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
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<ci> d_infinity </ci>
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<divide/>
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<ci> E </ci>
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<cn cellml:units="millivolt"> -6.1 </cn>
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<apply>
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<apply>
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<cn cellml:units="dimensionless"> 0.03 </cn>
<apply>
<plus/>
<ci> E </ci>
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</apply>
</apply>
</apply>
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<ci> d </ci>
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<apply>
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<apply>
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<ci> d_infinity </ci>
<ci> d </ci>
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<variable units="second" public_interface="in" name="time"/>
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<cn cellml:units="millivolt"> 6.6 </cn>
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<apply id="T_type_calcium_current_f_gate_tau_f_calculation">
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<apply>
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<apply>
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<apply>
<times/>
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<apply>
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<ci> E </ci>
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</apply>
</apply>
<apply id="T_type_calcium_current_f_gate_df_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> f </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> f_infinity </ci>
<ci> f </ci>
</apply>
<ci> tau_f </ci>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current">
<variable units="picoA" public_interface="out" name="i_Na"/>
<variable units="nanoS" name="g_Na" initial_value="250.0"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="E"/>
<variable units="dimensionless" private_interface="in" name="m"/>
<variable units="dimensionless" private_interface="in" name="h"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_Na_calculation">
<eq/>
<ci> i_Na </ci>
<apply>
<times/>
<ci> g_Na </ci>
<apply>
<power/>
<ci> m </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<ci> h </ci>
<apply>
<minus/>
<ci> E </ci>
<ci> E_Na </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_m_gate">
<variable units="dimensionless" public_interface="out" name="m" initial_value="0.0139"/>
<variable units="first_order_rate_constant" name="alpha_m"/>
<variable units="first_order_rate_constant" name="beta_m"/>
<variable units="millivolt" public_interface="in" name="E"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_m_calculation">
<eq/>
<ci> alpha_m </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_second"> 200.0 </cn>
<apply>
<plus/>
<ci> E </ci>
<cn cellml:units="millivolt"> 34.3 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.09 </cn>
<apply>
<plus/>
<ci> E </ci>
<cn cellml:units="millivolt"> 34.3 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_m_calculation">
<eq/>
<ci> beta_m </ci>
<apply>
<times/>
<cn cellml:units="first_order_rate_constant"> 8000.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.15 </cn>
<apply>
<plus/>
<ci> E </ci>
<cn cellml:units="millivolt"> 56.2 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="dm_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> m </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_m </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> m </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_m </ci>
<ci> m </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="fast_sodium_current_h_gate">
<variable units="dimensionless" public_interface="out" name="h" initial_value="0.0087"/>
<variable units="first_order_rate_constant" name="alpha_h"/>
<variable units="first_order_rate_constant" name="beta_h"/>
<variable units="millivolt" public_interface="in" name="E"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_h_calculation">
<eq/>
<ci> alpha_h </ci>
<apply>
<times/>
<cn cellml:units="first_order_rate_constant"> 32.4 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.14 </cn>
<apply>
<plus/>
<ci> E </ci>
<cn cellml:units="millivolt"> 93.4 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="beta_h_calculation">
<eq/>
<ci> beta_h </ci>
<apply>
<divide/>
<cn cellml:units="first_order_rate_constant"> 709.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<times/>
<cn cellml:units="dimensionless"> 4.2 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.06 </cn>
<apply>
<plus/>
<ci> E </ci>
<cn cellml:units="millivolt"> 45.4 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="dh_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> h </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_h </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> h </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_h </ci>
<ci> h </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifying_potassium_current">
<variable units="picoA" public_interface="out" name="i_K"/>
<variable units="picoA" public_interface="out" name="i_KK"/>
<variable units="picoA" public_interface="out" name="i_KNa"/>
<variable units="picoA_per_millimolar" name="Kk" initial_value="0.26"/>
<variable units="dimensionless" name="P_KNa" initial_value="0.035"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="E"/>
<variable units="dimensionless" private_interface="in" name="x"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_K_calculation">
<eq/>
<ci> i_K </ci>
<apply>
<plus/>
<ci> i_KK </ci>
<ci> i_KNa </ci>
</apply>
</apply>
<apply id="i_KK_calculation">
<eq/>
<ci> i_KK </ci>
<apply>
<times/>
<ci> x </ci>
<ci> Kk </ci>
<apply>
<power/>
<ci> Ko </ci>
<cn cellml:units="dimensionless"> 0.59 </cn>
</apply>
<apply>
<minus/>
<ci> Ki </ci>
<apply>
<times/>
<ci> Ko </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci> E </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_KNa_calculation">
<eq/>
<ci> i_KNa </ci>
<apply>
<times/>
<ci> x </ci>
<ci> Kk </ci>
<ci> P_KNa </ci>
<apply>
<power/>
<ci> Ko </ci>
<cn cellml:units="dimensionless"> 0.59 </cn>
</apply>
<apply>
<minus/>
<ci> Nai </ci>
<apply>
<times/>
<ci> Nao </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci> E </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="delayed_rectifying_potassium_current_x_gate">
<variable units="dimensionless" public_interface="out" name="x" initial_value="0.5682"/>
<variable units="dimensionless" name="x_infinity"/>
<variable units="second" name="tau_x"/>
<variable units="millivolt" public_interface="in" name="E"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="x_infinity_calculation">
<eq/>
<ci> x_infinity </ci>
<apply>
<divide/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<plus/>
<ci> E </ci>
<cn cellml:units="millivolt"> 25.1 </cn>
</apply>
<cn cellml:units="millivolt"> -7.4 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="tau_x_calculation">
<eq/>
<ci> tau_x </ci>
<apply>
<divide/>
<cn cellml:units="second"> 1.0 </cn>
<apply>
<plus/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 17.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.0398 </cn>
<ci> E </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.211 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.051 </cn>
<ci> E </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="dx_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> x </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> x_infinity </ci>
<ci> x </ci>
</apply>
<ci> tau_x </ci>
</apply>
</apply>
</math>
</component>
<component name="hyperpolarising_activated_current">
<variable units="picoA" public_interface="out" name="i_f"/>
<variable units="picoA" public_interface="out" name="i_fNa"/>
<variable units="picoA" public_interface="out" name="i_fK"/>
<variable units="millimolar" name="Kmf" initial_value="10.3"/>
<variable units="nanoS" name="g_fNa" initial_value="8.1"/>
<variable units="nanoS" name="g_fK" initial_value="13.5"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<variable units="millivolt" public_interface="in" name="E_K"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="second" public_interface="in" private_interface="out" name="time"/>
<variable units="millivolt" public_interface="in" private_interface="out" name="E"/>
<variable units="dimensionless" private_interface="in" name="y"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_f_calculation">
<eq/>
<ci> i_f </ci>
<apply>
<plus/>
<ci> i_fK </ci>
<ci> i_fNa </ci>
</apply>
</apply>
<apply id="i_fNa_calculation">
<eq/>
<ci> i_fNa </ci>
<apply>
<times/>
<ci> y </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Ko </ci>
<cn cellml:units="dimensionless"> 1.83 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> Ko </ci>
<cn cellml:units="dimensionless"> 1.83 </cn>
</apply>
<apply>
<power/>
<ci> Kmf </ci>
<cn cellml:units="dimensionless"> 1.83 </cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> g_fNa </ci>
<apply>
<times/>
<ci> Ko </ci>
<apply>
<minus/>
<ci> E </ci>
<ci> E_Na </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_fK_calculation">
<eq/>
<ci> i_fK </ci>
<apply>
<times/>
<ci> y </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Ko </ci>
<cn cellml:units="dimensionless"> 1.83 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> Ko </ci>
<cn cellml:units="dimensionless"> 1.83 </cn>
</apply>
<apply>
<power/>
<ci> Kmf </ci>
<cn cellml:units="dimensionless"> 1.83 </cn>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> g_fK </ci>
<apply>
<times/>
<ci> Ko </ci>
<apply>
<minus/>
<ci> E </ci>
<ci> E_K </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="hyperpolarising_activated_current_y_gate">
<variable units="dimensionless" public_interface="out" name="y" initial_value="0.0287"/>
<variable units="first_order_rate_constant" name="alpha_y"/>
<variable units="first_order_rate_constant" name="beta_y"/>
<variable units="millivolt" public_interface="in" name="E"/>
<variable units="second" public_interface="in" name="time"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="alpha_y_calculation">
<eq/>
<ci> alpha_y </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_second"> 0.36 </cn>
<apply>
<plus/>
<ci> E </ci>
<cn cellml:units="millivolt"> 137.8 </cn>
</apply>
</apply>
<apply>
<minus/>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 0.0666 </cn>
<apply>
<plus/>
<ci> E </ci>
<cn cellml:units="millivolt"> 137.8 </cn>
</apply>
</apply>
</apply>
<cn cellml:units="dimensionless"> 1.0 </cn>
</apply>
</apply>
</apply>
<apply id="beta_y_calculation">
<eq/>
<ci> beta_y </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="per_millivolt_second"> 0.1 </cn>
<apply>
<plus/>
<ci> E </ci>
<cn cellml:units="millivolt"> 76.3 </cn>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<exp/>
<apply>
<times/>
<cn cellml:units="dimensionless"> -0.21 </cn>
<apply>
<plus/>
<ci> E </ci>
<cn cellml:units="millivolt"> 76.3 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="dy_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> y </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> alpha_y </ci>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> y </ci>
</apply>
</apply>
<apply>
<times/>
<ci> beta_y </ci>
<ci> y </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_potassium_pump">
<variable units="picoA" public_interface="out" name="i_p"/>
<variable units="millimolar" name="KmNa" initial_value="40.0"/>
<variable units="millimolar" name="KmK" initial_value="1.0"/>
<variable units="picoA" name="i_pmax" initial_value="226.0"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="E"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_p_calculation">
<eq/>
<ci> i_p </ci>
<apply>
<times/>
<ci> i_pmax </ci>
<apply>
<divide/>
<ci> Nai </ci>
<apply>
<plus/>
<ci> Nai </ci>
<ci> KmNa </ci>
</apply>
</apply>
<apply>
<divide/>
<ci> Ko </ci>
<apply>
<plus/>
<ci> Ko </ci>
<ci> KmK </ci>
</apply>
</apply>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<power/>
<apply>
<divide/>
<apply>
<minus/>
<ci> E </ci>
<cn cellml:units="millivolt"> 40.0 </cn>
</apply>
<cn cellml:units="millivolt"> 211.0 </cn>
</apply>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sodium_calcium_exchange_current">
<variable units="picoA" public_interface="out" name="i_NaCa"/>
<variable units="picoA" name="kNaCa" initial_value="4000.0"/>
<variable units="dimensionless" name="x1"/>
<variable units="dimensionless" name="x2"/>
<variable units="dimensionless" name="x3"/>
<variable units="dimensionless" name="x4"/>
<variable units="dimensionless" name="k41"/>
<variable units="dimensionless" name="k34"/>
<variable units="dimensionless" name="k23"/>
<variable units="dimensionless" name="k21"/>
<variable units="dimensionless" name="k32"/>
<variable units="dimensionless" name="k43"/>
<variable units="dimensionless" name="k12"/>
<variable units="dimensionless" name="k14"/>
<variable units="dimensionless" name="Qci" initial_value="0.1369"/>
<variable units="dimensionless" name="Qn" initial_value="0.4315"/>
<variable units="dimensionless" name="Qco" initial_value="0.0"/>
<variable units="millimolar" name="K3ni" initial_value="26.44"/>
<variable units="millimolar" name="Kci" initial_value="0.0207"/>
<variable units="millimolar" name="K1ni" initial_value="395.3"/>
<variable units="millimolar" name="K2ni" initial_value="2.289"/>
<variable units="millimolar" name="Kcni" initial_value="26.44"/>
<variable units="millimolar" name="K3no" initial_value="4.663"/>
<variable units="millimolar" name="K1no" initial_value="1628.0"/>
<variable units="millimolar" name="K2no" initial_value="561.4"/>
<variable units="millimolar" name="Kco" initial_value="3.663"/>
<variable units="dimensionless" name="do"/>
<variable units="dimensionless" name="di"/>
<variable units="millimolar" public_interface="in" name="Cao"/>
<variable units="millimolar" public_interface="in" name="Nao"/>
<variable units="millimolar" public_interface="in" name="Cai"/>
<variable units="millimolar" public_interface="in" name="Nai"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="millivolt" public_interface="in" name="E"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_NaCa_calculation">
<eq/>
<ci> i_NaCa </ci>
<apply>
<times/>
<ci> kNaCa </ci>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> x2 </ci>
<ci> k21 </ci>
</apply>
<apply>
<times/>
<ci> x1 </ci>
<ci> k12 </ci>
</apply>
</apply>
<apply>
<plus/>
<ci> x1 </ci>
<ci> x2 </ci>
<ci> x3 </ci>
<ci> x4 </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="x1_calculation">
<eq/>
<ci> x1 </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> k41 </ci>
<ci> k34 </ci>
<apply>
<plus/>
<ci> k23 </ci>
<ci> k21 </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k21 </ci>
<ci> k32 </ci>
<apply>
<plus/>
<ci> k43 </ci>
<ci> k41 </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="x2_calculation">
<eq/>
<ci> x2 </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> k32 </ci>
<ci> k43 </ci>
<apply>
<plus/>
<ci> k14 </ci>
<ci> k12 </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k41 </ci>
<ci> k12 </ci>
<apply>
<plus/>
<ci> k34 </ci>
<ci> k32 </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="x3_calculation">
<eq/>
<ci> x3 </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> k14 </ci>
<ci> k43 </ci>
<apply>
<plus/>
<ci> k23 </ci>
<ci> k21 </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k12 </ci>
<ci> k23 </ci>
<apply>
<plus/>
<ci> k43 </ci>
<ci> k41 </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="x4_calculation">
<eq/>
<ci> x4 </ci>
<apply>
<plus/>
<apply>
<times/>
<ci> k23 </ci>
<ci> k34 </ci>
<apply>
<plus/>
<ci> k14 </ci>
<ci> k12 </ci>
</apply>
</apply>
<apply>
<times/>
<ci> k14 </ci>
<ci> k21 </ci>
<apply>
<plus/>
<ci> k34 </ci>
<ci> k32 </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="k43_calculation">
<eq/>
<ci> k43 </ci>
<apply>
<divide/>
<ci> Nai </ci>
<apply>
<plus/>
<ci> K3ni </ci>
<ci> Nai </ci>
</apply>
</apply>
</apply>
<apply id="k12_calculation">
<eq/>
<ci> k12 </ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci> Cai </ci>
<ci> Kci </ci>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci> Qci </ci>
</apply>
<ci> E </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<ci> di </ci>
</apply>
</apply>
<apply id="k14_calculation">
<eq/>
<ci> k14 </ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<power/>
<ci> Nai </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<times/>
<ci> K1ni </ci>
<ci> K2ni </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<power/>
<ci> Nai </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<times/>
<ci> K1ni </ci>
<ci> K2ni </ci>
<ci> K3ni </ci>
</apply>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> Qn </ci>
<ci> E </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<ci> di </ci>
</apply>
</apply>
<apply id="k41_calculation">
<eq/>
<ci> k41 </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> Qn </ci>
<ci> E </ci>
<ci> F </ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="di_calculation">
<eq/>
<ci> di </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> Cai </ci>
<ci> Kci </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci> Cai </ci>
<ci> Kci </ci>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> Qci </ci>
<ci> E </ci>
<ci> F </ci>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<apply>
<times/>
<ci> Cai </ci>
<ci> Nai </ci>
</apply>
<apply>
<times/>
<ci> Kci </ci>
<ci> Kcni </ci>
</apply>
</apply>
<apply>
<divide/>
<ci> Nai </ci>
<ci> K1ni </ci>
</apply>
<apply>
<divide/>
<apply>
<power/>
<ci> Nai </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<times/>
<ci> K1ni </ci>
<ci> K2ni </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<power/>
<ci> Nai </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<times/>
<ci> K1ni </ci>
<ci> K2ni </ci>
<ci> K3ni </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="k34_calculation">
<eq/>
<ci> k34 </ci>
<apply>
<divide/>
<ci> Nao </ci>
<apply>
<plus/>
<ci> K3no </ci>
<ci> Nao </ci>
</apply>
</apply>
</apply>
<apply id="k21_calculation">
<eq/>
<ci> k21 </ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<ci> Cao </ci>
<ci> Kco </ci>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> Qco </ci>
<ci> E </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<ci> do </ci>
</apply>
</apply>
<apply id="k23_calculation">
<eq/>
<ci> k23 </ci>
<apply>
<divide/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<power/>
<ci> Nao </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<times/>
<ci> K1no </ci>
<ci> K2no </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<power/>
<ci> Nao </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<times/>
<ci> K1no </ci>
<ci> K2no </ci>
<ci> K3no </ci>
</apply>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> Qn </ci>
<ci> E </ci>
<ci> F </ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<ci> do </ci>
</apply>
</apply>
<apply id="k32_calculation">
<eq/>
<ci> k32 </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<ci> Qn </ci>
<ci> E </ci>
<ci> F </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply id="do_calculation">
<eq/>
<ci> do </ci>
<apply>
<plus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<apply>
<divide/>
<ci> Cao </ci>
<ci> Kco </ci>
</apply>
<apply>
<times/>
<apply>
<divide/>
<ci> Cao </ci>
<ci> Kco </ci>
</apply>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<times/>
<ci> Qco </ci>
<ci> E </ci>
<ci> F </ci>
</apply>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<divide/>
<ci> Nao </ci>
<ci> K1no </ci>
</apply>
<apply>
<divide/>
<apply>
<power/>
<ci> Nao </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<times/>
<ci> K1no </ci>
<ci> K2no </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<power/>
<ci> Nao </ci>
<cn cellml:units="dimensionless"> 3.0 </cn>
</apply>
<apply>
<times/>
<ci> K1no </ci>
<ci> K2no </ci>
<ci> K3no </ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="background_sodium_current">
<variable units="picoA" public_interface="out" name="i_bNa"/>
<variable units="nanoS" name="g_Nab" initial_value="0.24"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="E"/>
<variable units="millivolt" public_interface="in" name="E_Na"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_bNa_calculation">
<eq/>
<ci> i_bNa </ci>
<apply>
<times/>
<ci> g_Nab </ci>
<apply>
<minus/>
<ci> E </ci>
<ci> E_Na </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="background_potassium_current">
<variable units="picoA" public_interface="out" name="i_bK"/>
<variable units="picoA_per_millimolar" name="KbK" initial_value="0.07"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="millivolt" public_interface="in" name="E"/>
<variable units="joule_per_mole_kelvin" public_interface="in" name="R"/>
<variable units="kelvin" public_interface="in" name="T"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Ki"/>
<variable units="millimolar" public_interface="in" name="Ko"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_bK_calculation">
<eq/>
<ci> i_bK </ci>
<apply>
<times/>
<ci> KbK </ci>
<apply>
<power/>
<ci> Ko </ci>
<cn cellml:units="dimensionless"> 0.41 </cn>
</apply>
<apply>
<minus/>
<ci> Ki </ci>
<apply>
<times/>
<ci> Ko </ci>
<apply>
<exp/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<ci> E </ci>
</apply>
<ci> F </ci>
</apply>
<apply>
<times/>
<ci> R </ci>
<ci> T </ci>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="sarcoplasmic_reticulum_kinetics">
<variable units="picoA" public_interface="out" name="i_up"/>
<variable units="picoA" public_interface="out" name="i_tr"/>
<variable units="picoA" public_interface="out" name="i_rel"/>
<variable units="picolitre" public_interface="out" name="V_rel" initial_value="0.015"/>
<variable units="picolitre" public_interface="out" name="V_up" initial_value="0.035"/>
<variable units="picoA" name="i_up_max" initial_value="21.2"/>
<variable units="first_order_rate_constant" name="alpha_rel"/>
<variable units="first_order_rate_constant" name="alpha_tr"/>
<variable units="millimolar" name="KmCaup" initial_value="0.0005"/>
<variable units="millimolar" name="KmCarel" initial_value="0.001"/>
<variable units="second" name="tau_rel" initial_value="0.005"/>
<variable units="second" name="tau_tr" initial_value="0.4"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="millimolar" public_interface="in" name="Cai"/>
<variable units="millimolar" public_interface="in" name="Caup"/>
<variable units="millimolar" public_interface="in" name="Carel"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="i_up_calculation">
<eq/>
<ci> i_up </ci>
<apply>
<times/>
<ci> i_up_max </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Cai </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> Cai </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<ci> KmCaup </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="i_tr_calculation">
<eq/>
<ci> i_tr </ci>
<apply>
<times/>
<ci> alpha_tr </ci>
<ci> Caup </ci>
</apply>
</apply>
<apply id="i_rel_calculation">
<eq/>
<ci> i_rel </ci>
<apply>
<times/>
<ci> alpha_rel </ci>
<ci> Carel </ci>
<apply>
<divide/>
<apply>
<power/>
<ci> Cai </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci> Cai </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
<apply>
<power/>
<ci> KmCarel </ci>
<cn cellml:units="dimensionless"> 2.0 </cn>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply id="alpha_rel_calculation">
<eq/>
<ci> alpha_rel </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_rel </ci>
<ci> F </ci>
</apply>
<ci> tau_rel </ci>
</apply>
</apply>
<apply id="alpha_tr_calculation">
<eq/>
<ci> alpha_tr </ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_rel </ci>
<ci> F </ci>
</apply>
<ci> tau_rel </ci>
</apply>
</apply>
</math>
</component>
<component name="ion_concentrations">
<variable units="millimolar" public_interface="out" name="Cai" initial_value="0.000034"/>
<variable units="millimolar" public_interface="out" name="Cao" initial_value="2.0004"/>
<variable units="millimolar" public_interface="out" name="Caup" initial_value="0.5832"/>
<variable units="millimolar" public_interface="out" name="Carel" initial_value="0.1101"/>
<variable units="millimolar" public_interface="out" name="Nai" initial_value="7.4994"/>
<variable units="millimolar" public_interface="out" name="Nao" initial_value="139.9929"/>
<variable units="millimolar" public_interface="out" name="Ki" initial_value="140.0073"/>
<variable units="millimolar" public_interface="out" name="Ko" initial_value="5.4243"/>
<variable units="picolitre" name="V_i" initial_value="2.5"/>
<variable units="picolitre" name="V_e" initial_value="0.5"/>
<variable units="second" name="tau_b" initial_value="0.1"/>
<variable units="millimolar" name="Nab" initial_value="140.0"/>
<variable units="millimolar" name="Cab" initial_value="2.0"/>
<variable units="millimolar" name="Kb" initial_value="5.4"/>
<variable units="second" public_interface="in" name="time"/>
<variable units="coulomb_per_millimole" public_interface="in" name="F"/>
<variable units="picoA" public_interface="in" name="i_bNa"/>
<variable units="picoA" public_interface="in" name="i_fNa"/>
<variable units="picoA" public_interface="in" name="i_Na"/>
<variable units="picoA" public_interface="in" name="i_p"/>
<variable units="picoA" public_interface="in" name="i_NaCa"/>
<variable units="picoA" public_interface="in" name="i_KNa"/>
<variable units="picoA" public_interface="in" name="i_KK"/>
<variable units="picoA" public_interface="in" name="i_fK"/>
<variable units="picoA" public_interface="in" name="i_bK"/>
<variable units="picoA" public_interface="in" name="i_CaL"/>
<variable units="picoA" public_interface="in" name="i_CaT"/>
<variable units="picoA" public_interface="in" name="i_up"/>
<variable units="picoA" public_interface="in" name="i_rel"/>
<variable units="picoA" public_interface="in" name="i_tr"/>
<variable units="picolitre" public_interface="in" name="V_rel"/>
<variable units="picolitre" public_interface="in" name="V_up"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="dNai_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Nai </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_bNa </ci>
<ci> i_fNa </ci>
<ci> i_Na </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> i_p </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> i_NaCa </ci>
</apply>
<ci> i_KNa </ci>
</apply>
</apply>
<apply>
<times/>
<ci> F </ci>
<ci> V_i </ci>
</apply>
</apply>
</apply>
<apply id="dNao_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Nao </ci>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> i_bNa </ci>
<ci> i_fNa </ci>
<ci> i_Na </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> i_p </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 3.0 </cn>
<ci> i_NaCa </ci>
</apply>
<ci> i_KNa </ci>
</apply>
<apply>
<times/>
<ci> F </ci>
<ci> V_e </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> Nab </ci>
<ci> Nao </ci>
</apply>
<ci> tau_b </ci>
</apply>
</apply>
</apply>
<apply id="dKi_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ki </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_KK </ci>
<ci> i_fK </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> -2.0 </cn>
<ci> i_p </ci>
</apply>
<ci> i_bK </ci>
</apply>
</apply>
<apply>
<times/>
<ci> F </ci>
<ci> V_i </ci>
</apply>
</apply>
</apply>
<apply id="dKo_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Ko </ci>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> i_KK </ci>
<ci> i_fK </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> -2.0 </cn>
<ci> i_p </ci>
</apply>
<ci> i_bK </ci>
</apply>
<apply>
<times/>
<ci> F </ci>
<ci> V_e </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> Kb </ci>
<ci> Ko </ci>
</apply>
<ci> tau_b </ci>
</apply>
</apply>
</apply>
<apply id="dCai_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Cai </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<apply>
<plus/>
<ci> i_CaL </ci>
<ci> i_CaT </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> -2.0 </cn>
<ci> i_NaCa </ci>
</apply>
<ci> i_up </ci>
<apply>
<minus/>
<ci> i_rel </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
<ci> V_i </ci>
</apply>
</apply>
</apply>
<apply id="dCao_dt">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Cao </ci>
</apply>
<apply>
<plus/>
<apply>
<divide/>
<apply>
<plus/>
<ci> i_CaL </ci>
<ci> i_CaT </ci>
<apply>
<times/>
<cn cellml:units="dimensionless"> -2.0 </cn>
<ci> i_NaCa </ci>
</apply>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> F </ci>
<ci> V_e </ci>
</apply>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> Cab </ci>
<ci> Cao </ci>
</apply>
<ci> tau_b </ci>
</apply>
</apply>
</apply>
<apply id="Caup_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Caup </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> i_up </ci>
<ci> i_tr </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_up </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
<apply id="Carel_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> Carel </ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci> i_tr </ci>
<ci> i_rel </ci>
</apply>
<apply>
<times/>
<cn cellml:units="dimensionless"> 2.0 </cn>
<ci> V_rel </ci>
<ci> F </ci>
</apply>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="membrane">
<component_ref component="L_type_calcium_current">
<component_ref component="L_type_calcium_current_d_gate"/>
<component_ref component="L_type_calcium_current_f_gate"/>
<component_ref component="L_type_calcium_current_f2_gate"/>
</component_ref>
<component_ref component="T_type_calcium_current">
<component_ref component="T_type_calcium_current_d_gate"/>
<component_ref component="T_type_calcium_current_f_gate"/>
</component_ref>
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_h_gate"/>
</component_ref>
<component_ref component="delayed_rectifying_potassium_current">
<component_ref component="delayed_rectifying_potassium_current_x_gate"/>
</component_ref>
<component_ref component="hyperpolarising_activated_current">
<component_ref component="hyperpolarising_activated_current_y_gate"/>
</component_ref>
<component_ref component="sodium_potassium_pump"/>
<component_ref component="sodium_calcium_exchange_current"/>
<component_ref component="background_sodium_current"/>
<component_ref component="background_potassium_current"/>
<component_ref component="sarcoplasmic_reticulum_kinetics"/>
<component_ref component="ion_concentrations"/>
</component_ref>
</group>
<group>
<relationship_ref relationship="encapsulation"/>
<component_ref component="L_type_calcium_current">
<component_ref component="L_type_calcium_current_d_gate"/>
<component_ref component="L_type_calcium_current_f_gate"/>
<component_ref component="L_type_calcium_current_f2_gate"/>
</component_ref>
<component_ref component="T_type_calcium_current">
<component_ref component="T_type_calcium_current_d_gate"/>
<component_ref component="T_type_calcium_current_f_gate"/>
</component_ref>
<component_ref component="fast_sodium_current">
<component_ref component="fast_sodium_current_m_gate"/>
<component_ref component="fast_sodium_current_h_gate"/>
</component_ref>
<component_ref component="delayed_rectifying_potassium_current">
<component_ref component="delayed_rectifying_potassium_current_x_gate"/>
</component_ref>
<component_ref component="hyperpolarising_activated_current">
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<rdf:li>Sinoatrial Node</rdf:li>
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The University of Auckland, Bioengineering Institute
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<vCard:Given>Socrates</vCard:Given>
<vCard:Family>Dokos</vCard:Family>
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<dc:title>
Ion Currents Underlying Sinoatrial Node Pacemaker Activity: A New
Single Cell Mathematical Model
</dc:title>
<bqs:volume>181</bqs:volume>
<bqs:first_page>245</bqs:first_page>
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<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
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<rdf:Description rdf:about="rdf:#a3f1b0a9-f509-4dd6-a940-84a4f6f37339">
<vCard:Given>Peter</vCard:Given>
<vCard:Family>Villiger</vCard:Family>
<vCard:Other>J</vCard:Other>
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<vCard:FN>Catherine Lloyd</vCard:FN>
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This is the CellML description of Dokos et al's 1996 mathematical
model of the ion currents underlying sinoatrial node pacemaker
activity. Please note that equations for reversal potentials were not included in the original published model and have had to be added.
Also, a current called i_KACh was included in the equations for
external and internal potassium ion concentration calculation. This
current had not been previously mentioned in the paper, and as i_KACh
is usually referred to in ischemic tissue, and also the background
potassium current i_bK had not been included in the equation, I am
assuming that this was a typo. The model authors have been contacted
and we are awaiting their reply.
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<vCard:Given>Branko</vCard:Given>
<vCard:Family>Celler</vCard:Family>
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<dcterms:W3CDTF>2002-07-18</dcterms:W3CDTF>
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<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
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<dcterms:W3CDTF>1996-08-07</dcterms:W3CDTF>
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Corrected equations: i_CaL_calculation in L_type_calcium_current and
i_CaT_calculation in T_type_calcium_current.
</rdf:value>
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<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="rdf:#615db5bb-ea20-4b08-8224-18de033ae4cc">
<dc:title>Journal of Theoretical Biology</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8a2e2cf3-dd8b-48f5-83fc-98e668694759">
<dcterms:W3CDTF>2003-04-10</dcterms:W3CDTF>
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<rdf:Description rdf:about="rdf:#771f8a1d-6d81-479b-b7cf-6aa5c72ff956">
<vCard:Given>Nigel</vCard:Given>
<vCard:Family>Lovell</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c2684e39-d841-423c-adb0-f74323a9ce58">
<dcterms:W3CDTF>2003-06-04</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#492f23bd-3b36-427b-96d2-e9c1a71e64c9">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
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<rdf:Description rdf:about="#dokos_celler_lovell_1996_version01">
<dc:title>
Dokos et al's 1996 mathematical model of the ion currents underlying
sinoatrial node pacemaker activity.
</dc:title>
<cmeta:bio_entity>Sinoatrial Node Cell</cmeta:bio_entity>
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<cmeta:species>Mammalia</cmeta:species>
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<dcterms:modified rdf:resource="rdf:#8d7547ba-0b98-4a14-9cc1-cfc8de5a5ebe"/>
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Made MathML id's unique
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<rdf:Description rdf:about="rdf:#424f995c-4597-4db7-9888-cb947031260e">
<dcterms:modified rdf:resource="rdf:#a77aabf3-34dc-47f1-a9bb-b6bb67c51d2a"/>
<rdf:value>
Added equations for k14, k41, di, k34, k21, k23, k32, and do in the sodium-calcium exchange current component.
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<cmeta:modifier rdf:resource="rdf:#e7cacc2b-d5ee-43ec-b3e2-c468011d84a0"/>
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<rdf:Description rdf:about="rdf:#8d7547ba-0b98-4a14-9cc1-cfc8de5a5ebe">
<dcterms:W3CDTF>2005-04-20</dcterms:W3CDTF>
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